This week in AP-Calculus, we learned implicit differentiation and how to find the derivatives of exponential, logarithmic, and the inverses of sin/cos/tan. It seemed like a lot to learn in one week, but it was basically just applying what we already knew about derivatives to solve for these kinds of problems. Those parts were easy during the week, but the implicit differentiation was a little different than what we been doing recently. Implicit functions are different than what we have been using because they contain y's and x's on both sides of the equation. Because of this, you have to solve these problems a little differently. First, you have to differentiate both sides with respect to x, so basically do what we have already been doing. Next, you have to collect the terms of dy/dx to one side of the equation. Just simple algebra to move things around to get all the dy/dx terms on one side. After that, you factor out the dy/dx from the one side. Then finally, you finish with solving for dy/dx. Super easy once you get the hang of it, because it just becomes the basics of derivatives, plus some basic algebra to rearrange the equation. This is finally the last bit of chapter 3 that we have to learn, since we have been working on this chapter for almost a month now. It will be nice to finally move on to the next chapter.
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February 2018
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